Existence of infinite models for law E5093

Determine whether the order‑5 equational law x ▷ y ▷ (y ▷ (y ▷ (x ▷ (z ▷ y)))) (equation E5093) admits any infinite magma models; either construct an explicit infinite model or prove that no infinite model exists.

Background

Kisielewicz showed that the law E5093 has no non-trivial finite models (an Austin identity), leaving open whether infinite models exist. The ETP provides context and partial classifications of order‑5 laws with infinite but no finite models.

The authors explicitly state that the existence of infinite models for E5093 remains an open question, highlighting a concrete target for further algebraic and model-theoretic investigation.

References

Does the law $x y (y (y (x (z y))))$ eq5093 have any infinite models? In it was shown that it has no non-trivial finite models, but the infinite model case was left as an open question.

— The Equational Theories Project: Advancing Collaborative Mathematical Research at Scale (2512.07087 - Bolan et al., 8 Dec 2025) in Conclusions and future directions (enumerated directions, item on Austin identities)